Quantum Machine Learning in Multi-Qubit Phase-Space Part I: Foundations
This addresses a foundational bottleneck in quantum machine learning for researchers, offering a novel theoretical framework.
The paper tackles the exponential growth of Hilbert space in quantum machine learning by constructing a phase-space formalism for multi-qubit systems, recasting dimensionality issues into linear scaling with qubit count and enabling variational modeling.
Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of the Hilbert space, QML faces practical limits in classical simulations with the state-vector representation of quantum system. On the other hand, phase-space methods offer an alternative by encoding quantum states as quasi-probability functions. Building on prior work in qubit phase-space and the Stratonovich-Weyl (SW) correspondence, we construct a closed, composable dynamical formalism for one- and many-qubit systems in phase-space. This formalism replaces the operator algebra of the Pauli group with function dynamics on symplectic manifolds, and recasts the curse of dimensionality in terms of harmonic support on a domain that scales linearly with the number of qubits. It opens a new route for QML based on variational modelling over phase-space.